@c ---content LibInfo---
@comment This file was generated by doc2tex.pl from d2t_singular/spectrum_lib.doc
@comment DO NOT EDIT DIRECTLY, BUT EDIT d2t_singular/spectrum_lib.doc INSTEAD
@c library version: (1.12.2.3,2002/03/06)
@c library file: ../Singular/LIB/spectrum.lib
@cindex spectrum.lib
@cindex spectrum_lib
@table @asis
@item @strong{Library:}
spectrum.lib
@item @strong{Purpose:}
  Singularity Spectrum for Nondegenerate Singularities
@item @strong{Author:}
S. Endrass

@end table

@strong{Procedures:}
@menu
* spectrumnd:: spectrum of nondegenerate isolated singularity f
@end menu
@c ---end content LibInfo---

@c ------------------- spectrumnd -------------
@node spectrumnd,,, spectrum_lib
@subsubsection spectrumnd
@cindex spectrumnd
@c ---content spectrumnd---
Procedure from library @code{spectrum.lib} (@pxref{spectrum_lib}).

@table @asis
@item @strong{Usage:}
spectrumnd(f[,1]); poly f

@item @strong{Assume:}
basering has characteristic 0 and local ordering,
@*f has isolated singularity at 0 and nondegenerate principal part

@item @strong{Return:}
@format
list S:
  ideal S[1]: spectral numbers in increasing order
  intvec S[2]:
    int S[2][i]: multiplicity of spectral number S[1][i]
@end format

@item @strong{Note:}
if a second argument 1 is given,
@*no test for a degenerate principal part will be done
@*SEE_ALSO: gaussman_lib

@cindex singularities
@cindex Gauss-Manin connection
@cindex spectrum
@end table
@strong{Example:}
@smallexample
@c computed example spectrumnd d2t_singular/spectrum_lib.doc:56 
LIB "spectrum.lib";
ring R=0,(x,y),ds;
poly f=x^31+x^6*y^7+x^2*y^12+x^13*y^2+y^29;
spectrumnd(f);
@expansion{} [1]:
@expansion{}    _[1]=-67/79
@expansion{}    _[2]=-62/79
@expansion{}    _[3]=-45/58
@expansion{}    _[4]=-57/79
@expansion{}    _[5]=-41/58
@expansion{}    _[6]=-55/79
@expansion{}    _[7]=-52/79
@expansion{}    _[8]=-37/58
@expansion{}    _[9]=-50/79
@expansion{}    _[10]=-18/29
@expansion{}    _[11]=-47/79
@expansion{}    _[12]=-45/79
@expansion{}    _[13]=-33/58
@expansion{}    _[14]=-16/29
@expansion{}    _[15]=-43/79
@expansion{}    _[16]=-42/79
@expansion{}    _[17]=-40/79
@expansion{}    _[18]=-1/2
@expansion{}    _[19]=-15/31
@expansion{}    _[20]=-14/29
@expansion{}    _[21]=-38/79
@expansion{}    _[22]=-27/58
@expansion{}    _[23]=-14/31
@expansion{}    _[24]=-35/79
@expansion{}    _[25]=-25/58
@expansion{}    _[26]=-13/31
@expansion{}    _[27]=-33/79
@expansion{}    _[28]=-12/29
@expansion{}    _[29]=-23/58
@expansion{}    _[30]=-31/79
@expansion{}    _[31]=-12/31
@expansion{}    _[32]=-30/79
@expansion{}    _[33]=-21/58
@expansion{}    _[34]=-11/31
@expansion{}    _[35]=-28/79
@expansion{}    _[36]=-10/29
@expansion{}    _[37]=-26/79
@expansion{}    _[38]=-19/58
@expansion{}    _[39]=-10/31
@expansion{}    _[40]=-25/79
@expansion{}    _[41]=-9/29
@expansion{}    _[42]=-17/58
@expansion{}    _[43]=-23/79
@expansion{}    _[44]=-9/31
@expansion{}    _[45]=-8/29
@expansion{}    _[46]=-21/79
@expansion{}    _[47]=-15/58
@expansion{}    _[48]=-8/31
@expansion{}    _[49]=-20/79
@expansion{}    _[50]=-7/29
@expansion{}    _[51]=-19/79
@expansion{}    _[52]=-18/79
@expansion{}    _[53]=-7/31
@expansion{}    _[54]=-13/58
@expansion{}    _[55]=-6/29
@expansion{}    _[56]=-16/79
@expansion{}    _[57]=-6/31
@expansion{}    _[58]=-15/79
@expansion{}    _[59]=-11/58
@expansion{}    _[60]=-14/79
@expansion{}    _[61]=-5/29
@expansion{}    _[62]=-13/79
@expansion{}    _[63]=-5/31
@expansion{}    _[64]=-9/58
@expansion{}    _[65]=-11/79
@expansion{}    _[66]=-4/29
@expansion{}    _[67]=-4/31
@expansion{}    _[68]=-10/79
@expansion{}    _[69]=-7/58
@expansion{}    _[70]=-9/79
@expansion{}    _[71]=-3/29
@expansion{}    _[72]=-8/79
@expansion{}    _[73]=-3/31
@expansion{}    _[74]=-7/79
@expansion{}    _[75]=-5/58
@expansion{}    _[76]=-6/79
@expansion{}    _[77]=-2/29
@expansion{}    _[78]=-2/31
@expansion{}    _[79]=-5/79
@expansion{}    _[80]=-3/58
@expansion{}    _[81]=-4/79
@expansion{}    _[82]=-3/79
@expansion{}    _[83]=-1/29
@expansion{}    _[84]=-1/31
@expansion{}    _[85]=-2/79
@expansion{}    _[86]=-1/58
@expansion{}    _[87]=-1/79
@expansion{}    _[88]=0
@expansion{}    _[89]=1/79
@expansion{}    _[90]=1/58
@expansion{}    _[91]=2/79
@expansion{}    _[92]=1/31
@expansion{}    _[93]=1/29
@expansion{}    _[94]=3/79
@expansion{}    _[95]=4/79
@expansion{}    _[96]=3/58
@expansion{}    _[97]=5/79
@expansion{}    _[98]=2/31
@expansion{}    _[99]=2/29
@expansion{}    _[100]=6/79
@expansion{}    _[101]=5/58
@expansion{}    _[102]=7/79
@expansion{}    _[103]=3/31
@expansion{}    _[104]=8/79
@expansion{}    _[105]=3/29
@expansion{}    _[106]=9/79
@expansion{}    _[107]=7/58
@expansion{}    _[108]=10/79
@expansion{}    _[109]=4/31
@expansion{}    _[110]=4/29
@expansion{}    _[111]=11/79
@expansion{}    _[112]=9/58
@expansion{}    _[113]=5/31
@expansion{}    _[114]=13/79
@expansion{}    _[115]=5/29
@expansion{}    _[116]=14/79
@expansion{}    _[117]=11/58
@expansion{}    _[118]=15/79
@expansion{}    _[119]=6/31
@expansion{}    _[120]=16/79
@expansion{}    _[121]=6/29
@expansion{}    _[122]=13/58
@expansion{}    _[123]=7/31
@expansion{}    _[124]=18/79
@expansion{}    _[125]=19/79
@expansion{}    _[126]=7/29
@expansion{}    _[127]=20/79
@expansion{}    _[128]=8/31
@expansion{}    _[129]=15/58
@expansion{}    _[130]=21/79
@expansion{}    _[131]=8/29
@expansion{}    _[132]=9/31
@expansion{}    _[133]=23/79
@expansion{}    _[134]=17/58
@expansion{}    _[135]=9/29
@expansion{}    _[136]=25/79
@expansion{}    _[137]=10/31
@expansion{}    _[138]=19/58
@expansion{}    _[139]=26/79
@expansion{}    _[140]=10/29
@expansion{}    _[141]=28/79
@expansion{}    _[142]=11/31
@expansion{}    _[143]=21/58
@expansion{}    _[144]=30/79
@expansion{}    _[145]=12/31
@expansion{}    _[146]=31/79
@expansion{}    _[147]=23/58
@expansion{}    _[148]=12/29
@expansion{}    _[149]=33/79
@expansion{}    _[150]=13/31
@expansion{}    _[151]=25/58
@expansion{}    _[152]=35/79
@expansion{}    _[153]=14/31
@expansion{}    _[154]=27/58
@expansion{}    _[155]=38/79
@expansion{}    _[156]=14/29
@expansion{}    _[157]=15/31
@expansion{}    _[158]=1/2
@expansion{}    _[159]=40/79
@expansion{}    _[160]=42/79
@expansion{}    _[161]=43/79
@expansion{}    _[162]=16/29
@expansion{}    _[163]=33/58
@expansion{}    _[164]=45/79
@expansion{}    _[165]=47/79
@expansion{}    _[166]=18/29
@expansion{}    _[167]=50/79
@expansion{}    _[168]=37/58
@expansion{}    _[169]=52/79
@expansion{}    _[170]=55/79
@expansion{}    _[171]=41/58
@expansion{}    _[172]=57/79
@expansion{}    _[173]=45/58
@expansion{}    _[174]=62/79
@expansion{}    _[175]=67/79
@expansion{} [2]:
@expansion{}    1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,\
   1,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1\
   ,1,1,2,1,1,1,1,2,1,1,1,1,1,2,1,4,1,2,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,1,2,1,\
   1,1,1,2,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1\
   ,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
@c end example spectrumnd d2t_singular/spectrum_lib.doc:56
@end smallexample
@c ---end content spectrumnd---
